$\ell$-torsion bounds for the class group of number fields with an $\ell$-group as Galois group
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- by Jürgen Klüners and Jiuya Wang PDF
- Proc. Amer. Math. Soc. 150 (2022), 2793-2805
Abstract:
We describe the relations among the $\ell$-torsion conjecture, a conjecture of Malle giving an upper bound for the number of extensions, and the discriminant multiplicity conjecture. We prove that the latter two conjectures are equivalent in some sense. Altogether, the three conjectures are equivalent for the class of solvable groups. We then prove the $\ell$-torsion conjecture for $\ell$-groups and the other two conjectures for nilpotent groups.References
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Additional Information
- Jürgen Klüners
- Affiliation: Universität Paderborn, Institut für Mathematik, Warburger Str. 100, 33098 Paderborn, Germany
- ORCID: 0000-0001-6825-307X
- Email: klueners@math.uni-paderborn.de
- Jiuya Wang
- Affiliation: Department of Mathematics, University of Georgia, Boyd Graduate Studies Research Center, Athens, Georgia 30601
- MR Author ID: 1296934
- ORCID: 0000-0002-8410-4274
- Email: jiuya.wang@uga.edu
- Received by editor(s): October 15, 2020
- Received by editor(s) in revised form: March 26, 2021, and October 5, 2021
- Published electronically: March 24, 2022
- Additional Notes: The second author was partially supported by Foerster-Bernstein Fellowship at Duke University
This project was accomplished during the Research in Pairs (RIP) program at Mathematisches Forschungsinstitut in Oberwolfach in 2019, supported by the Volkswagen-Stiftung - Communicated by: Rachel Pries
- © Copyright 2022 by the authors
- Journal: Proc. Amer. Math. Soc. 150 (2022), 2793-2805
- MSC (2020): Primary 11R29; Secondary 11R37, 11R45
- DOI: https://doi.org/10.1090/proc/15882
- MathSciNet review: 4428868